IDEAS home Printed from https://ideas.repec.org/p/duk/dukeec/10-72.html
   My bibliography  Save this paper

The Realized Laplace Transform of Volatility

Author

Listed:
  • Viktor Todorov
  • George Tauchen

Abstract

We introduce a new measure constructed from high-frequency financial data which we call the Realized Laplace Transform of volatility. The statistic provides a nonparametric estimate for the empirical Laplace transform of the latent stochastic volatility process over a given interval of time. When a long span of data is used, i.e., under joint long-span and fill-in asymptotics, it is an estimate of the volatility Laplace transform. The asymptotic behavior of the statistic depends on the small scale behavior of the driving martingale. We derive the asymptotics both in the case when the latter is known and when it needs to be inferred from the data. When the underlying process is a jump-diffusion our statistic is robust to jumps and when the process is pure-jump it is robust to presence of less active jumps. We apply our results to simulated and real financial data.

Suggested Citation

  • Viktor Todorov & George Tauchen, 2010. "The Realized Laplace Transform of Volatility," Working Papers 10-72, Duke University, Department of Economics.
    • Handle: RePEc:duk:dukeec:10-72
    as

    Download full text from publisher

    File URL: http://papers.ssrn.com/abstract=1687961
    File Function: main text
    Download Restriction: no
    ---><---

    Other versions of this item:

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cuchiero, Christa & Teichmann, Josef, 2015. "Fourier transform methods for pathwise covariance estimation in the presence of jumps," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 116-160.
    2. Todorov, Viktor & Tauchen, George & Grynkiv, Iaryna, 2014. "Volatility activity: Specification and estimation," Journal of Econometrics, Elsevier, vol. 178(P1), pages 180-193.
    3. Todorov, Viktor, 2021. "Higher-order small time asymptotic expansion of Itô semimartingale characteristic function with application to estimation of leverage from options," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 671-705.
    4. Li, Jia & Todorov, Viktor & Tauchen, George, 2016. "Inference theory for volatility functional dependencies," Journal of Econometrics, Elsevier, vol. 193(1), pages 17-34.
    5. Li, Gang & Zhang, Chu, 2016. "On the relationship between conditional jump intensity and diffusive volatility," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 196-213.
    6. Li, Jia & Patton, Andrew J., 2018. "Asymptotic inference about predictive accuracy using high frequency data," Journal of Econometrics, Elsevier, vol. 203(2), pages 223-240.
    7. Reiß, Markus, 2013. "Testing the characteristics of a Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2808-2828.
    8. Xinwei Feng & Lidan He & Zhi Liu, 2022. "Large Deviation Principles of Realized Laplace Transform of Volatility," Journal of Theoretical Probability, Springer, vol. 35(1), pages 186-208, March.
    9. Li, Jia & Todorov, Viktor & Tauchen, George & Chen, Rui, 2017. "Mixed-scale jump regressions with bootstrap inference," Journal of Econometrics, Elsevier, vol. 201(2), pages 417-432.
    10. Richard Y. Chen, 2018. "Inference for Volatility Functionals of Multivariate It\^o Semimartingales Observed with Jump and Noise," Papers 1810.04725, arXiv.org, revised Nov 2019.
    11. Kong, Xin-Bing & Liu, Cheng, 2018. "Testing against constant factor loading matrix with large panel high-frequency data," Journal of Econometrics, Elsevier, vol. 204(2), pages 301-319.
    12. Curato, Imma Valentina & Mancino, Maria Elvira & Recchioni, Maria Cristina, 2018. "Spot volatility estimation using the Laplace transform," Econometrics and Statistics, Elsevier, vol. 6(C), pages 22-43.
    13. Li, Jia & Todorov, Viktor & Tauchen, George, 2017. "Adaptive estimation of continuous-time regression models using high-frequency data," Journal of Econometrics, Elsevier, vol. 200(1), pages 36-47.
    14. Patrick Chang, 2020. "Fourier instantaneous estimators and the Epps effect," Papers 2007.03453, arXiv.org, revised Sep 2020.
    15. Xin-Bing Kong, 2017. "On the number of common factors with high-frequency data," Biometrika, Biometrika Trust, vol. 104(2), pages 397-410.
    16. B. Cooper Boniece & Jos'e E. Figueroa-L'opez & Yuchen Han, 2023. "Data-driven fixed-point tuning for truncated realized variations," Papers 2311.00905, arXiv.org, revised Oct 2024.
    17. Christensen, Kim & Thyrsgaard, Martin & Veliyev, Bezirgen, 2019. "The realized empirical distribution function of stochastic variance with application to goodness-of-fit testing," Journal of Econometrics, Elsevier, vol. 212(2), pages 556-583.
    18. Patrick Chang, 2020. "Fourier instantaneous estimators and the Epps effect," PLOS ONE, Public Library of Science, vol. 15(9), pages 1-24, September.
    19. Lidan He & Qiang Liu & Zhi Liu & Andrea Bucci, 2024. "Correcting spot power variation estimator via Edgeworth expansion," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(8), pages 921-945, November.

    More about this item

    Keywords

    Laplace transform; stochastic volatility; Central Limit Theorem; activity index; jumps; high-frequency data;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:duk:dukeec:10-72. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Department of Economics Webmaster (email available below). General contact details of provider: http://econ.duke.edu/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.